Найдите корень уравнения arccos4x+arccos2x=π/3

Question

Найдите корень уравнения arccos4x+arccos2x=π/3

Answer 1

Cos(arccos4x+arccos2x)=cosπ/3
cos(arccos4x)cos(arccos2x)-sin(arccos4x)sin(arccos2x)=1/2
4x*2x-√(1-16x²)*√(1-4x²)=1/2
8x²-1/2=√(1-20x²+64x^4)
64x^4-8x²+1/4=1-20x²+64x^4
20x²-8x²=3/4
12x²=3/4
x²=3/4:12
x²=1/16
x=-1/4
x=1/4